scholarly journals State Estimators for Uncertain Linear Systems with Different Disturbance/Noise Using Quadratic Boundedness

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Longge Zhang ◽  
Xiangjie Liu ◽  
Xiaobing Kong
Keyword(s):  
Linear Systems ◽  
Estimation Error ◽  
Measurement Noise ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
State Estimators ◽  
Sufficient Stability ◽  
Necessary And Sufficient ◽  
Uncertain Linear Systems ◽  
Sufficient Stability Conditions

This paper designs state estimators for uncertain linear systems with polytopic description, different state disturbance, and measurement noise. Necessary and sufficient stability conditions are derived followed with the upper bounding sequences on the estimation error. All the conditions can be expressed in the form of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the approach.

Convex Optimization Approach to Observer-Based Stabilization of Uncertain Linear Systems

2005 ◽  
Vol 128 (4) ◽  
pp. 989-994 ◽  
Author(s):  
Salim Ibrir
Keyword(s):  
Linear Systems ◽  
State Feedback ◽  
Observer Design ◽  
Linear Matrix ◽  
Computational Algorithms ◽  
Optimization Approach ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
The Stability ◽  
Uncertain Linear Systems

New sufficient linear matrix inequality conditions guaranteeing the stability of uncertain linear systems by means of dynamic output feedbacks are presented. It is shown that the search of an observer-based controller for this class of systems is fundamentally decomposed into two main problems: robust stability with a memoryless state feedback and observer design with measured uncertainties. Under the fulfilment of the developed linear matrix inequalities conditions, we show that the observer-based problem is solvable without any need for some equality constraints or iterative computational algorithms. Examples showing the potential of the results are presented.

scholarly journals ℋ∞Performance and Stability Analysis of Linear Systems with Interval Time-Varying Delays and Stochastic Parameter Uncertainties

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
M. J. Park ◽  
O. M. Kwon ◽  
Ju H. Park ◽  
S. M. Lee ◽  
E. J. Cha
Keyword(s):  
Stability Analysis ◽  
Linear Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Interval Time ◽  
Stochastic Parameter ◽  
Stochastic Properties ◽  
Random Change

This paper deals with the problems ofℋ∞performance and stability analysis for linear systems with interval time-varying delays. It is assumed that the parameter uncertainties are of stochastic properties to represent random change of various environments. By constructing a newly augmented Lyapunov-Krasovskii functional, less conservative criteria of the concerned systems are introduced with the framework of linear matrix inequalities (LMIs). Four numerical examples are given to show the improvements over the existing ones and the effectiveness of the proposed methods.

Analysis of Leveling Control System via Iterative Linear Matrix Inequalities with Full Order Observer

2012 ◽  
Vol 472-475 ◽  
pp. 1473-1476
Author(s):  
Jia Sun ◽  
Yu Hou Wu ◽  
Nan Xiao
Keyword(s):  
Control System ◽  
Design Procedure ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
State Variables ◽  
Linear Matrix Inequality Approach ◽  
Structural Uncertainties ◽  
Leveling Control ◽  
Uncertain Linear Systems ◽  
Iterative Linear Matrix Inequality

Abstract. This paper investigates leveling control system of suspended access platform using an observer-based controller. Uncertain linear systems for leveling control are derived and represented in terms of a set of matrix inequalities. In the system, all state variables needn’t be measured; the perturbations of leveling control are assumed to be described by structural uncertainties. The stiff problem is avoided since the design procedure is independent of the small parameter. The control problem can be effectively solved by the proposed iterative linear matrix inequality approach. The convergence of the algorithms is also studied. Furthermore, a numerical example and simulation results are given to illustrate the effectiveness of proposed method.

Impulsive finite-time observer design for uncertain positive linear systems with L2-gain analysis

2020 ◽  
Vol 42 (10) ◽  
pp. 1871-1881 ◽  
Author(s):  
Morteza Motahhari ◽  
Mohammad Hossein Shafiei
Keyword(s):  
Linear Systems ◽  
Finite Time ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
The State ◽  
Observer Design ◽  
Linear Matrix ◽  
Time Interval ◽  
State Variables ◽  
L2 Gain

This paper is concerned with the design of a finite-time positive observer (FTPO) for continuous-time positive linear systems, which is robust regarding the L2-gain performance. In positive observers, the estimation of the state variables is always nonnegative. In contrast to previous positive observers with asymptotic convergence, an FTPO estimates positive state variables in a finite time. The proposed FTPO observer, using two Identity Luenberger observers and based on the impulsive framework, estimates exactly the state variables of positive systems in a predetermined time interval. Furthermore, sufficient conditions are given in terms of linear matrix inequalities (LMIs) to guarantee the L2-gain performance of the estimation error. Finally, the performance and robustness of the proposed FTPO are validated using numerical simulations.

Mixed H2/H∞ Control for State-Delayed Linear Systems and a LMI Approach to the Solution of Coupled AREs

2003 ◽  
Vol 125 (2) ◽  
pp. 249-253 ◽  
Author(s):  
M. D. S. Aliyu
Keyword(s):  
Control Problem ◽  
Linear Systems ◽  
Linear Matrix Inequalities ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Riccati Equations ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Lmi Approach ◽  
Alternative Approach

In this paper, the state-feedback mixed H2/H∞ control problem for state-delayed linear systems is considered. Sufficient conditions for the solvability of this problem are given in terms of the solution to a pair of algebraic Riccati equations similar to the nondelayed case. However, these Riccati equations are more difficult to solve than those arising in the pure H2,H∞ problems, and an alternative approach is to solve a pair of linear matrix inequalities (LMIs).

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